Functional Equations and the Harmonic Relations for Multiple Zeta Values

Let $\theta (x)$ denote Jacobi's theta function. We show that the function $F_\xi (x) = (\theta '(0) \theta (x+\xi) )/ (\theta (x) \theta (\xi))$ satisfies functional equations, which is a generalization of the harmonic relations for multiple zeta values

Elliptic Bernoulli Functions And Their Identities

We introduce an elliptic analogue of the Bernoulli functions, which we call elliptic Bernoulli functions. They are defined by using the modified generating function of the elliptic polylogarithms. By degeneration of the elliptic Bernoulli functions, we obtain standard properties and new identities for the Bernoulli functions

Sums of Products of Kronecker's Double Series

Closed expressions are obtained for sums of products of Kronecker's double series. Corresponding results are derived for functions which are an elliptic analogue of the periodic Euler polynomials. As corollaries, we reproduce the formulas for sums of products of Bernoulli numbers, Bernoulli polynomials, Euler numbers, and Euler polynomials, which were given by K. Dilcher